On our Rome trip last fall, we booked a taxi for the morning we flew home, to get us to FCO 3 hours before the plane took off. We stayed in the historic Testaccio district, just west of the Circus Maximus, and the taxi only took a half hour - but that was before the sun had even come up, and there was very little traffic. Boy, those painful early morning flights!
I’d think allowing 45 minutes (starting for the airport at 6:45) will get you to the airport at the right time, even though you’re not needing to check bags. At least Italy’s got good coffee, and this is a time most people will need some!